Discuss the continuity and differentiability of `f(x)=e^(|x|)dot`

Explanation

`f(x)=e^{|x|} `

`f(x)={ e^{-x}, x<0 `and
`e^x, x geq 0}`

For the continuity at `x=0`

`f(0)=e^{0}=1`

`text { LHL }=lim _{x -> 0} f(x) `

`text{LHL}=lim _{h -> 0} f({O}-h) `

`text{LHL}=lim _{h -> 0} e^{-(0-h)} `

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